EXPONENTS, ATTRACTORS AND HOPF DECOMPOSITIONS FOR INTERVAL MAPS

被引:63
作者
KELLER, G [1 ]
机构
[1] UNIV ERLANGEN NURNBERG,INST MATH,W-8520 ERLANGEN,GERMANY
关键词
D O I
10.1017/S0143385700005861
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Our main results, specialized to unimodal interval maps T with negative Schwarzian derivative, are the following: (1) There is a set C(T) such that the omega-limit of Lebesbue-a.e. point equals C(T). C(T) is a finite union of closed intervals or it coincides with the closure of the critical orbit. (2) There is a constant-lambda-T such that lambda-T = limBAR(n --> infinity) 1/n log \(T(n))'(x)\ for Lebesgue-a.e. x. (3) lambda-T > 0 if and only if T has an absolutely continuous invariant measure of positive entropy. (4) lambda-T greater-than-or-equal-to inf {p-1 log \(T(p))'(z)\: T(p)Z = Z}, i.e. uniform hyperbolicity on periodic points implies-lambda-T > 0, and-lambda-T < 0 implies the existence of a stable periodic orbit.
引用
收藏
页码:717 / 744
页数:28
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